Method for safely and efficiently navigating magnetic devices in the body

ABSTRACT

A method of turning a medical device, having a magnetically responsive element associated with its distal end, at an operating point within an operating region inside a patient&#39;s body from an initial direction to a desired final direction, through the movement of at least one external source magnet. The at least one external source magnet is moved in such a way as to change the direction of the distal end of the magnetic medical device from the initial direction to the desired final direction without substantial deviation from the plane containing the initial direction and the desired final direction.

FIELD OF THE INVENTION

[0001] This invention relates to a method for navigating magneticdevices in the body, and in particular to a method for safely andefficiently navigating magnetic devices in the body using a moveablesource magnet outside the body.

BACKGROUND OF THE INVENTION

[0002] The navigation of magnetic medical devices, such as magnet-tippedguide wires, catheters, endoscopes, or other instruments, with a movablesource magnet presents several difficulties in ensuring that themovement of the medical device is as the physician expects and intends.The difficulties arise for several reasons, including the lag betweenthe direction of the magnetic field applied by the magnet and the actualdirection of the tip of the medical device, and “coning” of the tip ofthe medical device as it deviates from the intended plane of the turn asit turns.

SUMMARY OF THE INVENTION

[0003] According to one aspect of the invention, navigation of amagnet-tipped medical device takes into account the lag between thedirection of the magnetic field applied by the source magnet and actualdirection of the magnet tip. It is known that the magnet tip will lagthe exact direction of the magnetic field at its location by some finiteamount. This lag is the result of a restoring torque due to thestiffness of the attached device (e.g., the guidewire, catheter,endoscope, or other device to which the magnetic element is associated).

[0004] This creates an ambiguity between the applied magnetic field andthe actual direction of the magnet tipped device that can interfere withsafe and efficient navigation. The way this turn angle ambiguity isremoved is to provide a lead angle for the magnetic field which accountsfor the restoring, or turn-resisting, torque of the attached medicaldevice. According to one embodiment of this invention, information aboutthe restoring stiffness of the medical device to which the magnet isattached (e.g., a guidewire, catheter, endoscope or other device) isincluded in a computer program controlling the navigation. Informationof about the desired angle of turn and the desired radius (sharpness) ofthe desired turn can reside either in a lookup table or equationprogrammed in the computer. This information depends upon the propertiesof the device with which the magnet tip is associated, and thus will bedifferent for each different medical device. Given the magnitude of themoment of the tip magnet and this restoring torque, which is set equalto Γ, the value of B needed to achieve the required angle θ will follow.

[0005] According to a second aspect of this invention, it is desirableto make turns in such a way as to maintain the magnet tip of the medicaldevice in the same plane as the initial direction and the desired finaldirection, avoiding the problem of “coning” in which the magnet tipswings out of the plane of the turn. This is particularly important whenthe navigation is through the parenchyma, although even when navigatingthrough body lumens, such as blood vessels, maintaining planarity duringthe turn can be important. While the movement of the source magnetusually accurately aligns the tip of the medical device in the desiredfinal direction, the movement of the magnet does not necessarily movethe tip in the desired plane.

BRIEF DESCRIPTION OF THE DRAWINGS

[0006]FIG. 1 is a schematic diagram of a system for safely andefficiently navigating in accordance with this invention;

[0007]FIG. 2 is an enlarged schematic diagram of the source magnet andpatient;

[0008]FIG. 3 is a schematic view of the source magnet, showing some ofthe field lines;

[0009]FIG. 3A is a schematic view of the source magnet shown in FIG. 3after a rotation about Axis 2;

[0010]FIG. 4 is a schematic view of the source magnet with a polarcoordinate system superimposed at the center of the source magnet;

[0011]FIG. 5 is a vertical cross-sectional view of the source magnet,illustrating the magnetic field directions useful for a turn in an axialplane;

[0012]FIG. 6A is a top plan view of the source magnet, illustrating themagnetic field directions useful for a turn from an axial plane at pointA in FIG. 5;

[0013]FIG. 6B is a top plan view of the source magnet, illustrating themagnetic field directions useful for a turn from an axial plane at pointB in FIG. 5;

[0014]FIG. 7A is a perspective view of a single magnet system havingthree degrees of freedom, for implementing the method of the presentinvention;

[0015]FIG. 7B is a perspective view of the system shown in FIG. 7A withthe surface of constant magnetic field strength superposed thereon,illustrating some of the exclusion zones around which the magnet must bemaneuvered;

[0016]FIG. 7C is a perspective view of a single magnet system havingfive degrees of freedom, for implementing the method of the presentinvention;

[0017]FIG. 7D is a perspective view of the single magnet system shown inFIG. 7C, from a different angle;

[0018]FIG. 7E is a side elevation view of the single magnet system shownin FIG. 7C, showing a work envelope in which the single magnet can moveabove a patient, around the end of the patient, and below the patient;

[0019]FIG. 7F is a side elevation view of the single magnet systemshowing the magnet behind the patient's head and showing clearancerequired for the rotation of the single magnet;

[0020]FIG. 7G is a side elevation view of the single magnet systemshowing the magnet work envelope in which the single magnet cantranslate and rotates, in an annulus around a patient's body, and thesweep volume required to accommodate rotations of the single magnet inthe magnet work envelope;

[0021]FIG. 7H is a side elevation view of the single magnet systemshowing the source magnet rotated in cardiac to provide better accessfor the single magnet to the patient;

[0022]FIG. 7I is an end elevation view of the single magnet systemshowing the work envelope in which the source magnet can move in anannulus around a patient's head and showing the clearance between thework envelope of the magnet and the imaging system;

[0023]FIG. 8 is a schematic view showing the frames of reference of thesource magnet, the patient, and a locator device;

[0024]FIG. 9 is representation of the approximately spheroidal shape ofa surface of constant field strength for a magnet having axial symmetry;

[0025]FIG. 10 is a diagram of a constant field strength surface showingseveral trial moves of the source magnet useful in visualizing theefficient movement of the source magnet;

[0026]FIG. 11 is a schematic view a patient and a source magnet,illustrating coordinates and vectors useful in navigating;

[0027]FIG. 12 is diagram of the coordinates for the source magnet, shownin FIG. 11 illustrating the planes of rotation; and

[0028]FIG. 13 is a flow chart of the navigation inverse algorithm;

[0029]FIG. 14 is a cross sectional view of a typical coil source magnet38 showing a number of its magnetic field lines, and illustrating thegradient direction in two different locations;

[0030]FIG. 15A is a cross-sectional view of an aneurysm, showing therelative orientations of an applied magnetic field and an appliedmagnetic gradient before a gradient turn; and

[0031]FIG. 15B is a cross-sectional view of the aneurysm, showing therelative orientations of an applied magnetic field and an appliedmagnetic gradient after a gradient turn.

[0032] Corresponding reference numerals indicate corresponding partsthroughout the several views of the drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0033] In accordance with this invention, a magnetic medical device issafely and efficiently navigated in the body using an externally appliedmagnetic field. The navigation system 20 for implementing the methods ofthis invention is shown schematically in FIG. 1 as comprising a computer22 having a keyboard 24, mouse 26 and joystick 28 for inputting thephysician's instructions. Of course not all of these input devices arenecessary, and other input devices can be used as well. A display 30 isalso connected to computer 22 to allow the physician to operate thesystem and monitor the navigation. Imaging apparatus 32 is connected tothe computer, which processes the signals and displays images of theoperating region on the display 30. A controller 34 is connected to thecomputer for controlling an articulation mechanism 36 that moves thesource magnet 38. The magnet 38 in turn creates a magnetic field in theoperating region 40 of the patient, and more particularly at theoperating point 42 in the operating region, to control the orientationof a magnetic medical device 44 having a magnet tip 46.

[0034] The magnetic medical device 44 may be any medical device that thephysician wants to navigate in the body, for example a guide wire, acatheter, an endoscope, etc. The medical device 44 has a magnet tip 46associated with it that is of sufficient size and shape to be responsiveto an applied magnetic field and/or gradient from the external sourcemagnet 38 for navigating the medical device. The magnet tip 46 may be apermanent magnet or a permeable magnet. In this description, it isassumed that the magnet tip 46 is a permanent magnet, with the magnetfield aligned along the longitudinal axis of the magnet. One of ordinaryskill in the art could readily adapt this invention for use withpermanent magnets of other configurations, or for use with permeablemagnets.

[0035] In general, the magnetic medical device 44 is located at aparticular operating point 42 within a larger operating region 40 in thepatient. The operating region 40 is the region within the patient thatthe external source magnet 38 can apply a sufficient magnetic field toaffect the direction of the magnetic medical device 44.

[0036] The source magnet 38 may be a permanent magnet, but it ispreferably an electromagnet, and more preferably a superconductingelectromagnet. The source magnet 38 may actually comprise more than onemagnet. The source magnet 38 is mounted on an articulation device 36that can move the magnet 38. The articulation device 36 can translateand/or rotate the source magnet. In the simplest case the articulationdevice might permit two rotations of the source magnet, or perhaps tworotations of the magnet combined with a single translation, for exampletoward and away from the patient. In the most elaborate case, thearticulation device might permit two rotations of the source magnet, andthree translations of the source magnet in three mutually perpendiculardirections.

[0037] The imaging apparatus 32, may be, for example, bi-planarfluoroscopy equipment for imaging the operating region 40. Bi-planarfluoroscopy allows the location and sometimes the location and thedirection of the magnetic medical device 44 (or at least the distal endof the magnetic medical device) to be determined.

[0038] The invention relates to making a safe and proper turnefficiently. A proper turn is defined as one in which the distal end ofthe magnetic medical device 44 remains in the plane containing theinitial direction of the magnetic medical device and the desired finaldirection of the magnetic medical device. It is desirable to move thesource magnet 38 in such away as to effect the turning of the magneticmedical device 44 in a plane. There are typically a number of movementsof source magnet 38 that can turn the magnetic medical device 44 from agiven initial direction to the desired final direction. However, some ofthese possible movements will cause the magnetic medical device 44 tosweep out of the plane of the proper turn, in a motion known as “coning”that can unnecessarily disturb surrounding tissue. Others of thesepossible movements will be inefficient because of the significantmovement required of the source magnet 38. Still others of thesepossible movements will be prohibited by practical considerations, suchas limitations on the rotation or translation of the magnet,interference with the equipment surrounding the magnet and the patient,imaging equipment, and imaging beams. It is important to select a magnetmotion that is both safe, i.e. causes a “proper” turn, and efficient,i.e. one that is not unnecessarily of high complexity and long duration,

[0039] Lag From the Applied Magnetic Field

[0040] According to a first aspect of this invention, safe and efficientnavigation is achieved by taking into account the lag between the actualorientation of the medical device 44 and the orientation of the magneticfield applied by the source magnet 38. The magnetic torque vector isconventionally identified as r, and is given by the formula:

Γ=m×B  (1)

[0041] when m is the magnetic moment (a vector) of the magnet tip 46.The magnitude of this torque is Γ=mB sin θ, where m is the magnitude ofm, B the magnitude of B, and θ the angle between the vectors m and B.For a permanent magnet tip 46, with magnetization aligned in the usualway along its longitudinal axis, there is zero magnetic torque when themagnet tip is aligned exactly along B, and a maximum torque when themagnet tip 46 is perpendicular to (90 degrees away from) B.

[0042] Depending upon the size of a turn (or the radius of curvature ata point in a continuous path) and the stiffness of the attached device,a lead torque is needed to cause the magnet tip to turn in the correctdirection. Too much lead torque will turn the magnet tip too far, andtoo little lead torque will not adequately orient the magnet tip in theproper direction.

[0043] Where the magnet tip 46 is a permanent magnet, the moment m isfixed geometrically, but where the magnet tip is a permeable magnet, themoment m will rotate to an intermediate direction between the fielddirection and the longitudinal axis of the magnet tip. Therefore,equation (1) will apply exactly to the moment, but only inexactly to afixed geometrical aspect, say the axis, of an elongated permeablemagnetic tip. This is because m shifts with B in a permeable magnet. Inthe remainder of this description, it will be assumed that the magnettip 46 is a permanent magnet magnetized along its longitudinal axis,unless otherwise specified. A person of ordinary skill in the art couldreadily calculate characteristics of a permeable tip moment, and usethem in a similar fashion.

[0044] In making a turn, whether manually or automatically with the aidof a computer, the need for a lead torque must be anticipated. In oneembodiment of the present invention, information about the restoringstiffness of the medical device 44 to which the magnet tip 46 isattached (guidewire, catheter, endoscope, electrode, or other device) isincluded in the program controlling the navigation. Information aboutthe desired angle of turn and the desired radius (sharpness) of thedesired turn can reside either in a lookup table or equation programmedin the computer 22. This information depends upon the properties of themedical device 44 with which the magnet tip 46 is associated, and thuswill be different for each different medical device. Given the magnitudeof the moment of the magnet tip 46 and this restoring torque, which isset equal to Γ, the value of B needed to achieve the required angle θwill follow.

[0045] The desired angle of turn can be input, for example, using twopoint or three point navigation methods such as those disclosed inco-pending U.S. patent application Ser. No. 09/020,798, filed Feb. 9,1998 entitled “Device and Method for Specifying Magnetic Field forSurgical Applications”, incorporated herein by reference, or co-pendingU.S. patent application Ser. No. 09/370,067 filed Aug. 6, 1999, entitled“Method and Apparatus for Controlling Catheters in body Lumens andCavities”, incorporated herein by reference.

[0046] Making a Proper Turn

[0047] According to a second aspect of this invention, safe andefficient navigation is achieved by taking into account possibledeviations of the magnet tip 46 of a medical device 44 between theinitial direction and the desired final direction caused by the movementof the source magnet 38. Generally, the source magnet(s) 38 employed inmagnetic navigation are designed so as to have fields which can berepresented unambiguously. Moreover the articulation mechanism 36 formoving the source magnets 38 is designed to maneuver a source magnet toa position and orientation needed to apply the required field and/orgradient at the operating point 42 where the magnet tip 46 is located.The sometimes complex field shape of source magnet 38 generally demandsa complex approach to moving the source magnet to turn magnet tip 46,including translation and/or rotation of the source magnet. However,known symmetries of the source magnet 38 can reduce its complexity,cost, and weight of the articulation mechanism. For example, the fieldof a common solenoid coil has complete symmetry about its longitudinalaxis, and thus rotation about the longitudinal axis does not change thefield at the operating point in the patient. However, rotations abouttwo mutually perpendicular axes that are perpendicular to thelongitudinal axis can provide any change needed in the orientation ofthe magnetic field at the operating point. In general these tworotations, combined with one or more simple translations for locationalpurposes, can provide several alternate ways of changing the magneticfield vector at the operating point. While these alternatives providearticulation flexibility, they also make calculation of specificnavigation paths difficult.

[0048] It is convenient to focus on a coordinate system fixed in theframe of reference of the source magnet 38, and view the (ultimatelymoving) position and orientation of the magnet tip 46 in the patient asit moves in this frame when the magnet is rotated. The essence of thedesired turn will be to move the source magnet 38 in the patient frameof reference in a manner such that the magnetic field changes directionsmoothly and in the plane formed by the initial direction and thedesired final direction, i.e., the “proper turn” described above.

[0049] A first step in calculating a safe, efficient turn is thedefinition of the plane in which the magnet tip remains during the turn.This plane can be specified as a unit vector n perpendicular to it anddetermined from the equation

n=(V ₁ ×V ₂)/|(V ₁ ×V ₂)|  (2)

[0050] i.e., a unit vector along the direction of the cross product ofV₁ and V₂, where V₁ represents the initial direction and V₂ representsthe desired final direction.

[0051] The proper movement of the source magnet 38 may involvetranslations and/or rotations. The method incorporating “Euler angles”is a convenient and well-known tool for treating the rotations of anobject such as the source magnet. Goldstein, “Classical Mechanics”(Second Edition), Addison-Wesley Publishing Co. (1980), incorporatedherein by reference, describes matrix operations for keeping track ofvectors in such rotations. It is significant that these rotations are“noncommutative”, meaning that sequential rotations lead to a finaldirection which depends on the order of the individual componentrotations, i.e., the order of the rotations is important. Thisnoncommutative nature of rotational operations in mechanics must betaken into account when implementing rotations.

[0052] In the case of the static magnetic fields created by the sourcemagnets 38 preferably employed in this invention, the simplest possiblerotation which will provide a proper turn is chosen. Even so, such aturn, made with the simplest source magnet rotation and translation, butwithout full regard for the magnetic field shape, could result in amagnetic field vector progression at the operating point 42 at themagnet tip 46 which would lead to a turn with undesirable and possiblydangerous intermediate directions.

[0053] In FIG. 3, a source magnet 38, in the form of a simple coil, isshown with a few of its field lines, which are symmetrical about itslongitudinal axis (Axis 1). The initial position and orientation of tipmagnet 46 is represented by vector V_(1,) and the desired final positionand orientation of the tip magnet after a 90 degree turn is representedby vector V₂ after the turn. Each point on each field line of sourcemagnet 38 is a magnetic field vector B, and each field line is in aplane that that contains the coil axis (Axis 1) and is referred to as an“axial plane.”

[0054] Once the direction or directions of the required magneticfield(s) are known for a desired turn, a movement to cause the sourcemagnet 38 to apply the required field at the operating point 42 isdetermined. For simplicity in describing this second aspect of theinvention, it will be assumed that the magnet tip 46 will orient itselfexactly along a field line at its location. This implies that theinitial position before a turn, and the desired final position after aturn, lie along a field line of the source magnet 38. This assumptionthat V lies along B is important where, for example, the imaging systemused to monitor the procedure can only locate the position of the magnettip 46, and not its orientation. For simplicity in describing thissecond aspect of the invention, it is also assumed that the magnet tip46 is small enough to be represented approximately by a vector at apoint.

[0055] To illustrate the generally multiple sets of magnet motions thatcan accomplish a given turn in a patient, FIGS. 3 and 3A show twoalternate ways to rotate a field vector parallel to V₁ in a patient to anew direction parallel to V₂ at essentially the same point in thepatient. In FIG. 3 a translation of −V_(t) upward in the figure of thesource magnet 38 to relocate the operating point from B₁ to point B₃will accomplish this 90 degree turn of the field at a given point in thepatient.

[0056] In FIG. 3A the source magnet 38 is shown rotated clockwise 90degrees about Axis 2, which brings field point B₄ into a positionparallel to the desired direction V₂. It may or may not be necessary totranslate the source magnet 38 to bring the new location of B₄ to thestarting position of B₁, i.e., to the turning point in the patient.

[0057] The rotation and translation of the source magnet 38 preferablyoccur simultaneously, retaining the proper relationship betweentranslational speed and rotational angular velocity, so as to maintainthe field direction (with the magnet tip 46 crossing from field line tofield line of the source magnet 38 as necessary while the source magnetrotates and translates) so that the directional change of the fieldlines crossing the region between point V₁ and point V₂ smoothly turnthe magnet 46 as the medical device 44 progressed in feeding the magnettip forward through the turn. If the turn is very sharp, the vectorswould remain nearly at a point, and only change direction.

[0058] Depending on the capabilities of the articulation device for thesource magnet 38, one of the many possible movements (translation and/orrotation) of the magnet may be more efficient than the others. Forsimpler, less expensive articulation mechanisms, not all of the possiblemovements may be available. The selected movement can not always be themost efficient turn, and structural limitations of the magnet such asplacement of the cryocooler, power connections, etc., will sometimesprevent the use of the most efficient turn. In such cases a propermovement will not be the most efficient, but it should at least meet therequirement of maintaining the magnet tip in the plane of the turn.

[0059] As shown in FIG. 4, a spherical coordinate system is useful indescribing the position of the location of V₁ relative to the sourcemagnet 38. In this coordinate system, r is a vector from the center ofthe source magnet 38 to the operating point 42 (i.e., the location ofthe magnet tip 46); θ is the polar angle from the axis of the sourcemagnet (Axis 1) down to the line r; and φ is the azimuthal angle aroundAxis 1 of the plane of r and Axis 1, relative to an arbitrary fixedreference plane containing the axis. Because of axial symmetry of thefield of the source magnet, any motional change only in φ will result inno change in the field at V₁.

[0060] There are two types of planes in this coordinate system ofsignificant usefulness in visualizing the coordinates and motions. Thefirst type are the axial planes, which are any planes that contain boththe field line and the magnet axis. The second type are planesperpendicular to the axial plane. When this second type of plane lies onthe midplane of the magnet, it is referred to as the equatorial plane.Since rotation about the axis of the source magnet 38 (Axis 1) does notchange the field at a point, a useful totally orthogonal system wouldhave two other axes perpendicular to the source magnet's axis (Axis 1)and to each other. These axes are indicated as Axis 2 and Axis 3 in FIG.4, and they lie in the equatorial plane of the source magnet 38. Axes 2and 3 are shown schematically in FIG. 4, and could be physicallyimplemented with a gimbal apparatus to allow the source magnet to rotateabout these two axes. A usable articulation mechanism need only have twoof these three axes, and it would still be capable of turning the coilto any orientation, albeit with reduced freedom of intermediate motion.

[0061] A second major part of a turn is the calculation of theparticular magnet articulations for causing the magnetic field line(s)themselves to execute the proper turn. For this action (which wouldpreferably be implemented with a computer program) there must either bean equation or lookup tables of the magnetic field for every possibleorientation at every point in the operating region 40 in the patient. Anideal dipole, a special magnet with a simple equation for its field,illustrates this point. It will be appreciated that a more realisticequation (or a finite-element equivalent calculation) will also retainthe azimuthal symmetry of this magnet). In the magnet coordinate systemof FIG. 4, r=ix+jy+kz=ir sin θ cos φ+jr sin θ sin φ+kr cos θ, the fielda dipole is given by

B=(μ_(o)/4π)[−(m/r ³)+3(m·r)r/r ⁵]  (3)

[0062] where m is the moment of the dipole (now representing the sourcemagnet 38) and falls along the source magnet axis (by convention thez-axis), r is a vector between m (at the coil center) and the operatingpoint in the patient, and r is its magnitude. As shown in FIG. 4, m islocated and aligned along the z-axis in the most efficient use of thatcoordinate system. The dot product m·r is then mr cos θ, where m is themagnitude of the magnetic moment.

[0063] With the magnet tip 46 located at r in the source magnetcoordinate system and the initial vector directions and desired finalvector directions of the magnet field at that position, in both thesource magnet and patient coordinate systems, it is necessary during theturn to transform each incremental B in the source magnet coordinatesystem into B in the patient coordinate system while assuring that itsdirection remains in the plane of the proper turn. This can beimplemented with computer 22 having the full equation or a lookup tablewith an efficient search engine. The computer 22 must first establishthe location and orientation of the magnet tip 46 in the magnetcoordinate system, i.e., V₁. Then it must establish V₂ in thiscoordinate system, and the plane of rotation n_(a). This navigation willnow be described in more detail.

[0064] Two prototypical cases establish that any turn where the magnettip lies along a field line can be made through a combination oftranslations and rotations. In both of these cases the magnet tipstarting position is along a field line, and therefore in an axialplane. In the first such case, both V₁ and V₂ are oriented in an axialplane, and in the second characteristic case V₁ is oriented in an axialplane and V₂ is perpendicular to that plane. All other possible turnswhere the magnet tip initially lies along a field line can be consideredas some combination of these two special cases, with appropriatetrigonometric projections.

[0065] First Prototypical Case

[0066] In the first case where V₂ lies in a plane containing the axis orthe source magnet 38 (Axis 1) and V₁, then a rotation in that plane,which can be called the “starting plane” is necessary for a proper turn.As noted above, the vector direction of any plane is a vector of unitlength which is perpendicular to the plane. Rotation in this plane is arotation about a virtual axis perpendicular to that plane. This virtualrotation axis n_(a) is defined by analogy to equation 2:

n _(a)=(V ₁ ×V _(a))/|(V ₁ ×V _(a))|,  (4)

[0067] where V_(a) is a vector along the axis of the source magnet 38.This plane is chosen for convenience because it contains V₁, and it ismagnetically the same as any other plane containing the axis of thesource magnet 38. Therefore a vector V₁ located in a plane at anyazimuthal angle φ will satisfy equation (4) for this case. However, onlyrarely will n_(a) happen to be parallel to Axis 2 or Axis 3 of FIG. 4.Instead, the most general rotation can be formed from a trigonometriccombination of rotations about these two axes. For example, if the axisn_(a) were found in one case to be 45 degrees clockwise (looking down onthe coil) from Axis 2, it would mean that the front of the coil betweenAxis 2 and Axis 3 would tilt up to perform a clockwise rotation aboutthe n_(a) axis. Looking toward these axes, Axis 2 would rotatecounterclockwise, and Axis 3 would rotate clockwise (looking along thisunit vector). In this case, both axes would rotate at the same angularrates.

[0068]FIG. 5 illustrates this turn in an axial plane (with V₁ and V₂separated by an exaggerated distance). The starting point is labeled A,and B and C identify two other points around that field line whichpasses through A. For clarity, only a single field line is shown. (Thecircular shape shown for the field line is not intended to be a highlyaccurate representation of the shape of a field line from a real coil.)The plane of turn, designated by n_(a), is oriented out of the page.

[0069] The field line at point B is parallel to V₂, and a simpletranslation of the source magnet 38 to bring point B to the location ofV₂ would accomplish a turn of the magnet tip 46 in the patient. However,the translation would have to be judiciously chosen on some curve inorder for the field strength to remain unchanged during the turn. It isdesirable that the field strength remain constant to reduce variationsin the direction of the magnet tip 46. Moreover, the translational pathshould lie in the starting plane. With these choices, the turn would bea proper one, albeit probably not efficient. To accomplish this turn,the translational path would be determined by moving from point A topoint B in the field line of equation (3) or an accurate line calculatedfor a real coil, and then translating the source magnet in the inversedirection of that path. To maintain the curve as a proper turn wouldinvolve a choice of fixed φ. An obvious choice for an efficient(although perhaps not the most efficient) proper turn in this case wouldbe a translation with φ and magnitude B fixed at each step of the turnand with θ changing smoothly and monotonically.

[0070] Second Prototypical Case

[0071] In the second prototypical case, V₁ is in an axial plane but V₂is perpendicular to that plane so that rotation about a differentvirtual axis n₂ is necessary. Since n_(a) still defines the startingplane, the vector axis of rotation, n₂, is perpendicular to both V₁ andn_(a)

n ₂=(V ₁ ×n _(a))/|(V ₁ ×n _(a))|  (5)

[0072] Two turns for this second general case are illustrated in FIGS.6A and 6B, which are views looking down on the axis of the source magnet38. A first turn of the second prototypical case is illustrated in FIG.6A where the starting location is shown as a projection of point A ofFIG. 5 onto this view. The field rotation is shown as n₂, out of thepaper.

[0073] It is apparent that a pure rotation of the source magnet 38 aboutits axis, needed to accomplish n₂, cannot be effective for this properturn because of field line symmetry. A translation, approximately alongAxis 3 and in direction T, would bring the magnet tip 46 to point A′ inthe frame of reference of the source magnet 38, as shown by the straightdashed line, and would accomplish a proper turn. However, since thedistance between the path and the source magnet axis varies, the fieldstrength will vary during such a turn. Instead, a translation of thesource magnet 38 in which point A progressed in a circle around thesource magnet axis, would result in a proper turn with constant fieldmagnitude. Such a path is shown as a dot-dashed line 50. (This is thetrajectory of the magnet tip 46 in the frame of reference of the sourcemagnet. The movement of the source magnet 38 in the operating room willbe opposite to this motion and is show as dot-dashed line 52).

[0074] A second turn of the second prototypical case is illustrated inFIG. 6B, where V₁ is again in the axial plane, but now is located aspoint B of FIG. 5, i.e., pointing into the paper in this view. Now n₂points away from the coil. This turn is the simplest, and isaccomplished purely by rotating the coil about the axis from the centerof the magnet out to the location of V₁. For generality, this is shownas different from Axis 2 or Axis 3. Such an axis is establishedtrigonometrically in the same manner as described above. (A prior purerotation about the coil axis could establish one of these as the turnaxis without disturbing the magnet tip, but with some simplerarticulation mechanisms, such a rotation might have been consideredgenerally unnecessary and therefore not available).

[0075] Having established the qualitative nature of proper turns, we nowdescribe quantitative means of calculating the magnet articulationsneeded for navigation. Navigation in the operating region of the patientwould intuitively seem to be most directly visualized and calculated inthe patient reference system. This would, however, entail transformationof the rotating and translating magnetic source field into thatreference system, which would be difficult, given that the source magnetfield often cannot be put into analytical form. (A lookup table of fivedimensions could contain all transformations to follow, but is just amodification of the following method). While transforming a field fromone frame of reference to another can be complex, any specific magneticfield vector is easily transformed between the coordinate systems. Thismethod has been devised to avoid the difficulty of fieldtransformations. It provides ways to test trial turns for propercharacteristic, and to break up a full turn as necessary to maintain theturn in a sufficiently close planar form. In addition, an essentialfeature in this method is a means of removing the ambiguity of a turn,i.e., a method of limiting the possibilities to a small, practical“neighborhood” of trial turns, and then choosing the “best” proper turnfrom among the possible trial turns.

[0076] The procedure works in the reference frame of the source magnetafter the desired vector in the patient coordinate frame is transformed,and then calculates and transforms each necessary field vector into thepatient frame. Sometimes this can be done automatically with searchmethods and equations. The procedure can involve steps in purelyrotating a field vector through a turn from V₁ to V₂ in the patientframe, using operations in the source magnet frame, and taking care thatthese operations take into account when a rotation in that frame will inaddition require a translation of the source magnet 38 in the patientframe. For the method to work, the relationship between the two framesmust be known. An external locating means can be provided to connect thelocation and orientation of the frame of reference of the source magnetto the patient frame. One example of such a locating means is disclosedin Van Steenwyk et al., U.S. Pat. No. 4,173,228, issued Nov. 6, 1979,for Catheter Locating Device, incorporated herein by reference. In thefollowing description, and as shown in FIG. 8, unprimed coordinates (x,y, z) will designate the patient frame, and primed coordinates (x′, y′,z′) are in the source magnet frame. Third, coordinates (x″, y″, z″) areused for the room coordinates, i.e., the coordinates in which thelocator device is fixed. In one embodiment, the locator deviceestablishes the relationship between the magnet tip on the medicaldevice and the source magnet, as described above. In another embodiment,the locator device might establish the relationship between the sourcemagnet and a point on a patient, fixed in the room, in which case theorientation of the magnet tip 46 would have to be determined in someother way. Bi-planar fluoroscopic imaging can locate the magnet tip 46,but does not always give good information about its orientation.Commercial magnetic field locators are available which can also find theorientation of the magnet tip 46. Other imaging systems can usecombinations of imaging modalities. In the following discussion, anyappropriate locating and/or imaging devices can be used.

[0077] Generally, the transformation problem has five degrees of freedom(although, depending upon the application, it is not necessary that thearticulation device must have all of these degrees of freedom). Thetranslation of a vector between two reference frames has 3 components,and the rotation of a vector has 2 components (polar and azimuthalangles). The field vectors to be transformed need not be rotated aroundan axis which is collinear with their own directions.

[0078] Two types of vectors have been discussed. Vectors which yield theposition of an object in a reference frame, and vectors which describe amagnetic field at a point. These are treated separately and explicitlybelow.

[0079] The operating position location in each frame of reference can bespecified as a vector relative to the origin in that frame of reference,and a positional transformation in a given frame is then a vectoraddition or subtraction. (There is no need to rotate the positionvectors except when dealing with exclusion zones.) However, the fieldvectors must in general be rotated and translated. In the patient frame,the location vector is simply a vector from a fixed origin in that frameout to the operating point (where the magnet tip 46 is located). In theframe of the source magnet 38, however, the origin for the locationvector will change each time the source magnet is translated, asdescribed below. FIG. 8 shows frame axes in these frames plus thelocator frame. With some location methods, the origin of the patientframe could be at the operating point 42 where the magnet tip 46 islocated, and would move as that point moved. A locator system operatingthroughout the duration of the procedure would maintain informationabout the locations of (0, 0, 0) and (0′, 0′, 0′) relative to its ownfixed frame (0″, 0″, 0″).

[0080] The location and direction of vector V₁ in the frame of referenceof the patient is transformed into V₁′ in the frame of reference of themagnet source 38 by well known vector algebraic methods. In general thiswill require separate vector translation and rotation operations.(Translations involve vector sums or differences, rotations involvematrix multiplication.) Given V₁, the three coordinates of the positionof the vector V₁′ are found by simple addition of the known coordinateorigin transformation from (0, 0, 0) to (0′, 0′, 0′). The neededinformation is known, as stated above, from external locating means. Ofcourse, if the external locating means is operating continuously, thisstep will be immediate and trivial. Otherwise, any magnet movement androtation since an initial “calibrating” relative location andorientation by that locating means will necessarily have been recordedin the processor and will be accounted for. In either case, one morestep is necessary. The vector V₁′ must be located relative to (0′, 0′,0′), and its orientation must also be found. If V₁ is the very firstvector in the procedure V₁, will be found in the calibration justmentioned. Otherwise, V₁ will be known in the processor, which mustcontinually account for each step of a procedure, and within certainaccuracy can retain a “dead reckoning” of translations and rotations ofthe source magnet 38, as well as translation and rotation of the magnettip 46.

[0081] It is sometimes necessary and usually desirable in navigation forthe magnetic field strength to remain constant. This provides a usefulconstraint on the navigation calculations. One of ordinary skill in theart would know how to change the magnetic field strength, if needed,given this method for a turn made at constant field strength. In theconstant field strength method, the location of V₁′ would always fall ona surface of constant field strength. For a typical single sourcemagnet, such a surface would be calculable, and would approximate anaxially symmetric spheroid.

[0082]FIG. 9 illustrates a surface 100 of constant field strength for asource magnet 38, along with a few vectors 102 on each of several“latitude planes” 104. It is seen that on a given latitude plane theaxial symmetry of the magnet assures that the field line vectors 102make a constant angle with the surface 100, and also with the magnetaxis. Each field line lies in a plane which contains the magnet axis.Thus changes in field direction, on the constant field surface, requiresome component of motion along a longitudinal line.

[0083] Once the relative locations of V₁ and V₁′ are determined,rotations are made in the “forward direction,” V₁ to V₁′, by standardmatrix means. For example, Goldstein equation (4-46) shows such atransformation using Euler angles (φ, θ, ψ) in one turn sequenceconvention. This reference also discusses several other suchconventions. The particular rotation convention used for (φ, θ, ψ) inthis invention is arbitrary, but once chosen for the initial calibrationit must be retained. A convenient choice might use the axes of rotationsprovided by the articulation mechanism. “Reverse” rotations, say fromV₁′ to V₁, are then given by an inverse matrix, Goldstein equation(4-47). It is to be understood that the angles (φ, θ, ψ) are not anglesthrough which the source magnet will actually turn, but rather are usedin the algorithm to calculate the transformation between a vector in thetwo reference frames. Instead, the actual magnet turns will consist ofsimple small vector rotations, with added translation if needed tomaintain the vector position of the magnet tip 46 in the patient frame.

[0084] The movements of the source magnet for a proper turn arepreferably first carried out “virtually” in a computer processor 22.Once the path for the movements of the source magnet is determined,execution of the path will require instructions to the controller 34 ofthe magnet articulation mechanism 36. Algorithms for calculating theangles and translational position of the magnet needed to provide a nextV (i.e., a next B) are described below:

[0085] A. Once V₁ is located, the desired turn to V₂ is input by thephysician according to one of the standard means of communicating to theprocessor system. Examples of methods of inputting desired turns aredisclosed in U.S. utility patent application Ser. No. 09/020,798, filedFeb. 9, 1998 entitled “Device and Method for Specifying Magnetic Fieldfor Surgical Applications”, incorporated herein by reference, orco-pending U.S. patent application Ser. No. 09/370,067 filed Aug. 6,1999, entitled “Method and Apparatus for Controlling Catheters in BodyLumens and Cavities”, incorporated herein by reference.

[0086] B. The movement of the source magnet to effect the turn from V₁to V₂ is determined. This is conveniently done with a computerprocessor. The angle by which the direction of the magnet tip 46 variesfrom the plane containing V₁ and V₂ is then determined. If this amountdoes not exceed a predetermined threshold for acceptable deviation,e.g., 5 degrees, then the articulation mechanism 36 can be operated bycontroller 34 under the direction of the computer processor 22 to makethe determined movement of the source magnet 38. If the turn from V₁ toV₂ is small, for example, 10 degrees or less, it is likely that only onestep of the turn is needed, as any coning during the turn will be smallenough that it generally will not interfere with navigation. However, ifthe amount by which the direction of the magnet tip 46 varies from theplane of V₁ and V₂ by more than the predetermined threshold, then theturn is broken up into a number of sub-turns. Of course, sub-turns couldbe used automatically, without testing whether they are needed.

[0087] C. If subturns are employed, the final vector V₂ is labeledV_(n), and a number of intermediate vectors V₁ (i=2, 3, . . . , n−1) aredetermined by the processor 22. One method of determining theseintermediate vectors is to make an even-sized division of the angle ofturn, constraining each individual vector to be in the plane formed byV₁ and V_(n). Other methods of determining these intermediate vectorsinclude unequal divisions of the turn angle based upon where the magnettip direction deviates from the desired plane of the turn by more thanthe predetermined threshold, or some lesser value. Of course there arenumerous other methods for determining the intermediate vectors.

[0088] D. The vectors V₁, V₂, . . . , V_(n) in the patient frame ofreference are transformed to V₁′, V₂′, . . . , V_(n)′ in the sourcemagnet frame of reference by a pure forward rotation. In general, V₁′,V₂′, . . . , V_(n)′ will not lie in a plane, even if V₁, V₂, . . . ,V_(n) did. Each pair of angles, V₁′, V₂′, or V₂′,V₃′, etc. will form aplane, which can be determined as in equation (2) above. Resultingrotations V₁ to V₂, or V₂ to V₃, etc. will not generally lie in a singleplane, but since these are small rotations they will have acceptableindividual coning, by decision of step 2 above. Choice of the startingvector in the patient plane, however, will assure that the overall turnis nearly planar.

[0089] E. The processor 22 then determines a movement of the magnet foreach of the sub-turns. When the magnet makes a rotation from V_(i) toV_(i+1), the point on the constant field surface will in general move,i.e., translate relative both to (0′, 0′, 0′) and to (0, 0, 0). Also,the magnet rotation needed to make this small turn, will not in generalbe uniquely determined, which is common with inverse problems. Theprocessor will calculate such a translation for the small angle rotationV_(i) to V_(i+1), using a series of trial rotations in a plane tangentto the surface at the initial point, in the neighborhood of the vectorV_(i), as shown in FIG. 10. In general, each vector associated with arotation shown in this frame, corresponds to a rotation and translationof the point in the patient reference frame. That is, as the fieldvector position in the magnet frame changes from P_(i) to P_(i+1) due torotation in the magnet frame, the reverse transformed position in thepatient frame will need in addition to translate if the originalrotation in the patient frame [Goldstein equation (4-46)] is totransform back correctly. That means that the source magnet 38 mustsimultaneously be translated to maintain the magnetic field vectorposition constant in the patient frame. Only moves with some componentalong a longitude line will change the field vector direction. However,it will sometimes be found that the most efficient step for a small turnwill also have some component of rotation along a latitude line, whenaccount is taken of the transformation into patient coordinates. Foreach trial the processor will calculate the translation inferred in thepatient frame. For the trial chosen as optimum, the magnet will have tomake the inverse of this translation, in order to keep the vectorlocation fixed in the patient frame.

[0090] F. The processor selects from the trial rotations one which ismost efficient, i.e., the trial which requires the smallest translationof the magnet to accomplish the (partial) turn in the patient framewithout a translation in the patient frame. A weighting algorithm can bedeveloped based upon the “costs” of certain rotations over otherrotations, certain translations over other translations, and ofrotations over translations.

[0091] Practical articulators and magnet systems will have limitedrotations, say 360 degrees or 720 degrees, because of leads, and otherattachments. They also will have limitations of motions because ofinterference of the magnet and its accoutrements with the patient, withimaging equipment and imaging beams, or with other medical equipment.Such limitations can be transformed from the patient reference frame tothe source magnet reference frame and entered into the processor 22controlling the navigation as an exclusion region. Preferably thelimitations can be entered as a series of vectors X₁,X₂, . . . , X_(n)describing a surface in the patient frame, which transform to X₁′,X₂′, .. . , X_(n)′ in the source magnet frame. These can be chosen withsufficiently small angular spacing as to provide a means of forming asmooth sheet of exclusion boundary in the magnet frame, which is used bythe processor to execute limits on magnet motion.

[0092] When the magnet housing and accoutrements present a highlyasymmetrical front toward the patient and interfering equipment, theexclusion sheet will be dynamic, i.e. a joint overlap of sheets for thepatient region and for the magnet region will be needed to preventinterference.

[0093] G. The final and all intermediate step vectors (V₂′, . . .V_(n)′) will be calculated before the execution of a turn. When, in anyturn, the final (or any intermediate) step vector falls beyond anexclusion limit, or near it, the processor 22 can choose to reorient thesource magnet, using its symmetry, if helpful, to move safely away fromincursion of the limit. Clearly, for safety the limit surface can havebeen chosen conservatively “inside” a true limit surface.

[0094] H. The processor 22 also confirms that the rotations will notcause the direction of the magnet tip to vary from the plane of V₁ andV_(n) by more than the predetermined threshold. If it does, theprocessor re-selects some or all of the intermediate vectors (V₂′, . . .V_(n−1)′), and repeats the process.

[0095] I. The processor 22 will then cause the articulating mechanism 36to turn and/or translate the source magnet 38 successively through theangles from V₂′ . . . , V_(n)′, which will turn the angle in the patientfrom through V₂, . . . V_(n−1) to V_(n).

[0096] Common matrix transformations can be used for conversion betweenthe patient reference frame and the source magnet reference frame. Onetechnique includes the steps of:

[0097] 1. Characterize the field of the source magnet 38 by measuring itover the sample volume of interest at sufficient resolution thatinterpolation will not yield significant errors.

[0098] 2. Putting the source magnet field information into a computerfunction B_(m)(x_(m),y_(m),z_(m)) (x′, y′, z′ as shown in FIG. 8), orequivalent lookup table, where x_(m), y_(m), and z_(m) are expressed inmagnet coordinates and B_(m) is the magnetic field vector.

[0099] 3. Compute the transformation matrix T_(mp) for converting ageneral vector B from magnet to patient coordinates.

[0100] 4. Invert this matrix to T_(mp) ⁻¹.

[0101] 5. Compute x_(m), ym, z_(m) by feeding T_(mp) ⁻¹ into a generalminimization function that moves around the magnet on its constraints(e.g., where there are three degrees of freedom, 2 rotations and 1translations) and using a forward calculation function:

B _(p)(x _(p) ,y _(p) ,z _(p))=T _(mp) ⁻¹ B _(m)(x _(m) ,y _(m) ,z _(m))

[0102] Such a routine would rapidly converge unless the magnet shapeand/or shielding presented fields which are pathological (not monotonicin the vicinity of the required components). Such magnet designs shouldbe avoided. Where there are more degrees of freedom, this will involvesearching over the surplus degrees of freedom to minimize the requiredmovement (rotation and translation) of the source magnet.

[0103] Navigating with a Single Magnet

[0104] When the determination of magnet rotations for a safe turn hasbeen made by the previously described steps, instructions to the chosenrobotic articulation mechanism 36 for magnet positions and rotations tobe achieved in a turn, or partial turn, are needed. These algorithms canbe put into two categories, those involving magnets with axial symmetryand those without axial symmetry. In addition, it is possible to havepractical modalities of operation for symmetrical magnets which takeadvantage of the symmetry to simplify the magnet articulations, and touse fewer numbers of degrees of freedom in them. Three preferredmodalities will be described: (A) is an efficient, highly specific3-degree of freedom navigation for an axially symmetric magnet, with aflow chart for the inversion of the field in the source magnetcoordinates to the field in the patient coordinates shown in FIG. 13;(B) is a more general 3-degree of freedom method which covers the makingof turns; and (C) is a general 5-degree of freedom algorithm by whichthe greater articulation flexibility provides for better handling ofexclusion boundaries in which the magnet cannot move.

[0105] (A) 3-Degree of Freedom Navigation for an Axially SymmetricMagnet

[0106] It can be seen that one of ordinary skill in the art can extendthe specific information of this example (A), especially the explicitdefinitions and diagrams, in a manner to provide different versions ofthe present means, or any more general modality of navigation by usingdifferent numbers of rotations and/or translations.

[0107]FIG. 11 is a diagram showing a patient, a single magnet source ofexternal magnetic field, the location for a small magnet tip to beguided in a medical procedure, and the definition of a few of thecoordinates and vectors to execute the above-described type ofnavigation in one preferred embodiment. At the magnet tip location oroperating point 42 specified by r′ (also by point P) a magnetic field Bis to be applied with given magnitude and orientation to create a turn.

[0108]FIG. 12 shows additional useful parameters and defines coordinatesfor the single magnet and field point (the operating point representedby position vector r′) at which the field vector B is to be specified,and which is to be provided by the articulated magnet. It also showsplanes which make the geometric attributes of this motion easier tovisualize.

[0109] The magnet position in this three degree-of-freedom problem isuniquely specified by the offset z_(o) (distance of the center of thecoil from the closest point of patient anatomy), and the polar andazimuth angles made by the magnet symmetry axis z_(m) relative to thetranslated patient coordinate system (x, y, z′) system.

[0110] For a coil having axial symmetry this method shows how to makethe search for one degree of freedom trivial by using an analyticalexpression for one of the variables. This method takes advantage of thefact that the field vector B must lie in the plane defined by thevectors z_(m) and ρ_(m), due to the cylindrical symmetry of the sourcemagnet (either a coil magnet or a permanent magnet).

[0111] Referring to FIGS. 11 and 12 for a supine patient, the y-z planeis horizontal, x is vertical, y is horizontal to the patient's right,and z is along the patient body axis. A second set of coordinates isused, where x, y, z′ with origin O′ is displaced along z by an amountz_(o) from the patient origin O shown in FIG. 11. Thus the x,y,z andx,y,z′ planes are vertical and are perpendicular to the patient bodyaxis, at the top of the patient's head and through the magnet center,respectively.

[0112] The operating point 42 (or P) is at r′ in the x, y, z′ coordinatesystem. θ_(o), φ_(o) are the spherical polar coordinates of B in asystem with polar axis along z′, and azimuthal angle measured from thex,z′ plane. In FIG. 12, B is shown both at its true location P and atthe origin O′ where these angles can be shown clearly. θ_(a), φ_(a) arethe polar and azimuthal angles of the magnet axis z_(m), in the samespherical polar coordinate system as the patient frame, with the polaraxis along z and the azimuth measured in the x,y plane and relative tothe x-axis.

[0113] z_(m), ρ_(m) are the cylindrical coordinates of the operatingpoint 42 in an axially symmetric magnet coordinate system, correspondingto the vectors z_(m), ρ_(m). The field point at x, y, z′, specified asthe vector r′, is identified as P. The point of intersection of a lineparallel to the z-axis and passing through P with the line of projectionof r′ on the x, y plane, is identified as A. The polar angle of r′ inpatient coordinates is identified as θ′. The polar angle of r′ in magnetcoordinates is identified as β. The point on the z-axis at z_(o)+z isidentified as K. There are three parallelograms defining three planes:The first, O'APK is a parallelogram which forms a plane perpendicular tothe x, y plane and going through both the z-axis and the field point P.r′ falls in this plane. The rotation of this plane about the z-axis isby angle φ′ with respect to the x-z plane. The second, O'ρ_(m)Pz_(m) isa parallelogram which forms a plane containing the field point P and theaxes z_(m) and ρ_(m). r′ also falls in this plane and therefore thisvector forms the axis of intersection of the two planes. By itsdefinition z_(m) is the projection of r′ on the axis of the coil. Notonly the field point P, but the field vector B lies in this plane, whichis an axial plane of the magnet (a plane containing a complete fieldline and the magnet axis). r′, and therefore both parallelograms, rotateabout z as the field point changes in azimuth in the patientcoordinates. The second parallelogram is in general tilted relative tothe first. The third plane is the plane formed by B and the line PA.This plane is in general oblique to the first and second planes.

[0114] As defined, φ_(a) is a precession angle of the magnet axis, theazimuthal rotation about z (measured from the x,z plane) of the line ofthe projection of vector z_(m) representing the magnet axis, on the x-yplane.

[0115] The algorithm is implemented in the following steps (derivationand details are given later):

[0116] 1. Specify coordinates (x, y, z) of a field point in thenavigation volume of the patient.

[0117] 2. Specify the magnitude of the desired magnetic field B, and adesired accuracy for this magnitude.

[0118] 3. Specify the polar and azimuth angles θ_(o) and φ_(o) of thedesired B vector.

[0119] 4. Specify an accuracy for the dot product between the specifiedand computed B unit vectors.

[0120] 5. Search on the magnet azimuth coordinate φ_(a) as follows:

[0121] a. For each φ_(a), search on the magnet offset, z_(o).

[0122] b. For each pair φ_(a), z_(o), calculate the magnet polar angle,θ_(a), which is required to insure that the B vector lies in the z-r′plane.

[0123] c. Continue the search on the offset z_(o) until the computedcoil field magnitude is equal to B to within the desired accuracy.

[0124] d. Using this offset, and the set of azimuth and polar magnetangles, compute the B vector at the field point

[0125] e. Form the dot product between the computed and specified Bvectors. Form the dot product of unit vectors by dividing by the vectormagnitudes.

[0126] f. When this dot product is equal to unity to within thespecified accuracy, the inverse calculation is complete

[0127] 6. Calculate the changes in z_(o), φ_(a) and θ_(a) from theirpresent positions.

[0128] 7. Calculate a sequence of these variables which will provide thechanges proportionately.

[0129] 8. Send the sequence to the magnet articulation device 36 toeffect the determined movement of the source magnet 38.

[0130] In summary, the method searches magnet azimuth and magnet offset,computes a polar angle that insures that the B vector lies in a planecontaining the magnet axis and the field point vector, selects an offsetthat insures the correct magnitude of B, and completes the azimuthsearch when the computed and specified B vectors are aligned in space.

[0131] The derivation and details of this Example A are as follows: Thevectors r′, z_(m), and B are given in their polar representations by:

r′=r′[sin θ′ cos φ′i+sin θ′ sin φ′j+cos θ′k]  (5)

z _(m) =z _(m)[sin θ_(a) cos φ_(a) i+sin θ_(a) sin φ_(a) j+cos θ_(a)k]  (6)

B=B[sin θ_(o) cos φ_(o) i+sin θ_(o) sin φ_(o) j+cos θ_(o) k],  (7)

[0132] The angles of the position vector r′ are given in terms of itsCartesian coordinates by:

φ′=tan⁻¹(y/x)  (8)

θ′=tan⁻¹{[{square root}(x ² +y ²)]/(z+z _(o))},  (9)

[0133] and,

r′={square root}[x ² +y ²+(z+z _(o))²].  (10)

[0134] The polar and azimuth angles θ_(a) and φ_(a) of the magnet axisare unknowns to be determined. The polar and azimuth angles of the Bvector, θ_(o) and φ_(o), are specified by the user, or are calculatedfrom its Cartesian representation.

[0135] The polar angle θ_(a) can be computed mathematically in terms ofthe other angles by imposing the condition that the B vector lie in thez_(m)−r′−ρ_(m) plane. This condition is necessitated by the symmetry ofthe coil. It is stated mathematically as the null dot product of B witha vector perpendicular to that plane

B·(z _(m) ×r′)=0.  (11)

[0136] Insertion of the defining equations (1) to (3) into (7), andnoting that the magnitudes of the vectors drop out, we have an equationwhich can be solved for the tangent of the polar angle:

θ_(a)=tan⁻¹{[sin θ′ sin θ_(o) sin(φ′−φ_(o))]/[cos θ_(o) sin θ′sin(φ′−φ_(a))+cos θ′ sin θ_(o) sin(φ_(a)−φ_(o))]}  (12)

[0137] The field components relative to the magnet are given by:

B(r′)=B _(ρ)(ρ_(m) , z _(m))ρ_(m)/ρ_(m) +B _(z)(ρ_(m) ,z _(m))z _(m) /z_(m)  (13)

[0138] where a numerical coil field algorithm computes B_(ρ) and B_(z),given the coordinates z_(m) and ρ_(m). From FIG. 12 the magnitude of thez and ρ components of the vector r′ are:

z_(m)=r′ cos β  (14)

ρ_(m)=r′ sin β,  (15)

[0139] where the angle β is measured in the z_(m)−r′−ρ_(m) plane and canbe found from vector operations to be:

cos β=sin η_(a) sin θ′ cos(φ_(a)−φ′)+cos θ_(a) cos θ′  (16)

sin β={square root}(1−cos²β).  (17)

[0140] The computed magnitude of the field in magnet components is

B={square root}(B _(ρ) ² +B _(z) ²),  (18)

[0141] and this expression is used in the algorithm to search the magnetoffset, z_(o), where equations (12) to (17) are used to compute equation(18) for each value of Z_(o).

[0142] Finally, the search on the magnet axis azimuth is terminated whenthe specified B vector and the B vector computed from Equation (13) arealigned in space to within a given accuracy. Appropriate expressions forthe unit vectors in terms of the patient Cartesian coordinates are:

z _(m) /z _(m)=sin θ_(a) cos φ_(a) i+sin θ_(a) sin φ_(a) j+cos θ_(a)k  (19) $\begin{matrix}{{\rho_{m}/\rho_{m}} = {{{\left( {r^{\prime} - z_{m}} \right)/\rho}\quad m} = {{\left\lbrack {{\left( {{\sin \quad \theta^{\prime}\quad \cos \quad \varphi^{\prime}} - {\cos \quad \beta \quad \sin \quad \theta_{a}\cos \quad \varphi_{a}}} \right)/\sin}\quad \beta} \right\rbrack i} + {\left\lbrack {{\left( {{\sin \quad \theta^{\prime}\sin \quad \varphi^{\prime}} - {\cos \quad \beta \quad \sin \quad \theta_{a}\sin \quad \theta_{a}\sin \quad \varphi_{a}\sin \quad \varphi_{a}}} \right)/\sin}\quad \beta} \right\rbrack j} + {\left\lbrack {{\left( {{\cos \quad \theta^{\prime}} - {\cos \quad \beta \quad \cos \quad \theta_{a}}} \right)/\sin}\quad \beta} \right\rbrack k}}}} & (20)\end{matrix}$

[0143] The specified and computed unit vectors are obtained fromequations (7) and (13) by dividing by the specified field magnitude andfield magnitude computed by Equation (18), respectively. When their dotproduct is equal to unity, within the specified accuracy, the azimuthsearch is complete.

[0144] The solution offset, polar and azimuthal angles z_(o), θ_(a), andφ_(a) are then used to articulate the magnet to acquire the desiredfield B.

[0145]FIG. 13 is a flow chart of a program which executes the algorithmjust presented to provide the inverse calculation for articulating amagnet having axial symmetry. A preferred embodiment of a more generalsearch which allows an incremental proper rotation of a field vector ispresented below in example (B). An outline of an embodiment for ageneral 5-degree-of-freedom search is also presented below in example(C). One versed in the art will see how to modify these to provideinversion algorithms to articulate a magnet with any number of degreesof freedom greater than 3.

[0146] (B) Navigation with 3-Degree of Freedom Searches

[0147] The algorithm outlines a method which operates directly withtransformation matrices, but requires a full 3-parameter search.

[0148] Magnet Insertion

[0149] 1. Locate the current magnet tip location, r′ (i.e. the operatingpoint 42 or P) in the patient frame.

[0150] 2. Input the desired starting field direction, B, in patientcoordinates.

[0151] 3. Using appropriate transformations, and a search sequence,calculate the necessary magnet axis rotational angles, φ and θ, andtranslation axis position to achieve B at r′.

[0152] 4. Execute magnet axis rotations φ and θ.

[0153] 5. Execute translation to calculated position.

[0154] After the source magnet has been inserted

[0155] 1. Locate the current magnet tip location, r′, in the patientframe.

[0156] 2. Translate the magnet along the z-axis to bring the operatingpoint 42 or P where the magnet tip 46 is located, to the desired fieldstrength line of the magnet.

[0157] 3. Calculate the desired new magnetic field direction B₂ inpatient reference frame at the operating point P or 42 where the magnettip 46 is located.

[0158] 4. Input the new desired magnetic field direction, B₂, in patientcoordinates.

[0159] 5. Create a set of vectors in the patient reference frame thatlink B₁ to B₂ at the operating point 42 or P that lie in the planecreated by B₁ and B₂.

[0160] 6. Calculate the necessary magnet axis rotations, φ and θ, andtranslation that produces the set of vectors found in step #5.

[0161] 7. Execute movement with the 3 variables synchronized.

[0162] In a practical device for implementing the method of example (B),such as the one shown in FIGS. 7A and 7B, the azimuthal rotation mightbe limited to 360°, the polar rotation limited to 180°, and the Z-axistranslation might be limited to 8.5 inches to about 14.5 inches. Motionis selected to avoid possible problem with navigation due to rotationalstops in azimuthal direction.

[0163] (C) Navigation with 2 Rotational and 3 Translational Degrees ofFreedom

[0164] This outlines a method of using two additional translationalmotions which can give flexibility to avoiding interferences withpatient and imaging equipment and beams. Such a method might beimplemented by the device shown in FIG. 7C. By choosing specific x and yaxis translations at the outset, the problem again becomes completelydetermined. If other constraints are more valuable in a specificapplication, these can be replaced.

[0165] 1. Locate the current magnet tip location, P

[0166] 2. Translate in the x y plane (x-axis and y-axis) such that thetip position and the center of the magnet coil define a line parallel tothe z-axis of translation.

[0167] 3. Translate along the z-axis to bring the current tip location,P, to the desired field strength line.

[0168] 4. Calculate the magnetic field direction, B₁, at the tiplocation P.

[0169] 5. Input the desired new field direction, B₂.

[0170] 6. Create a set of field vectors that link B₁ to B₂ at P, andwhich lie in the plane of B₁ to B₂.

[0171] 7. Calculate the necessary magnet rotations, φ and θ, andtranslation (z-axis only), for the set of vectors created in step 6.

[0172] 8. Execute source magnet movement.

[0173] Use of Gradients

[0174] Navigation in accordance with this invention can be conducted insuch a way as to use the source magnets to pull the medical device inaddition to orienting the distal end of the medical device. Magneticforce is generated by the rate of change of magnetic field strength withposition. This is commonly called a “magnetic gradient” even though avector magnetic field does not have a gradient in the usual mathematicalsense. As is well known to one of ordinary skill in the art, a magneticfield is a vector field, and a gradient operates only on a scalar field,that is a scalar function of position. What is usually meant by gradientis not gradient of the magnetic field, but the gradient of a scalarproduct of the magnetic moment vector m of the tip, and the magneticfield vector B at its location, i.e., (m·B). What is intended here, andgenerally in magnetic work, is the application of the force equation

F=∇(m·B)  (21)

[0175] Assuming a small magnetic tip 46, the moment can be treated as apoint. This assumption is adequately met when the magnetic field changesover a distance appreciably larger than the size of the magnet tip. Thusthe gradient operator acts on the scalar product m·B, the positiondependent product of the magnet tip moment projected on the field B, atany given point. The direction of this force need not be along eitherthe field direction B or the direction of the moment m. Rather it is inthe direction in which the product m·B changes most rapidly.

[0176] It is the purpose of this aspect of the invention to navigate amagnetic medical device with a magnet tip safely to a location andorientation in a patient so that the magnetic gradient which falls atthat point will pull the tip in a desired direction. FIG. 14 shows across section containing the axis of a typical coil source magnet 38with a number of its magnetic field lines. The arrows on the field linesshow the direction of the magnetic field B at points along each line. Inaddition, the gradient of the field is shown in two locations, at pointsA and B, by double arrows. The directions of the arrows show thedirections that a free small magnet would be pulled at those twolocations. The direction of pull on a free magnet is in the direction inwhich the field lines are becoming denser, which is also the directionin which the field is increasing in strength. This is because a freemagnet will align its moment with B, and remain aligned as it is pulled.

[0177] Thus the product m B becomes simply the arithmetic product of themagnitudes of the two vectors, mB. But in practice a small magnet tip 46on a magnetic medical device is not totally free, rather it is somewhatrestrained by the device with which it is associated, as well as anysurrounding tissue with which it is in contact. For example, catheters,guidewires, and electrodes etc. all have inherent stiffness that wouldrestrain the alignment of the magnet tip with the field direction, inwhich case the product m·B will be somewhat smaller than mB, which isthe maximum possible value.

[0178] In FIG. 14, a free magnet tip 46 at point A will be oriented withits moment aligned along the field which is along the axis of the sourcemagnet 38, and the magnet will be pulled along the same direction. Thisis the “longitudinal gradient” or alternatively the “longitudinalfield.” It is also sometimes called an “axial gradient.” At point B thefree magnet tip 46 will have its moment m aligned along B and thereforeparallel to the magnet axis, but the gradient will pull the magnet tiptowards the source magnet as shown by the arrow, i.e., perpendicular tothe source magnet axis. This is called a “transverse gradient,” oralternatively a “transverse field.” In some medical applications (e.g.,pulling a linear electrode to an inner wall of a heart chamber, orpulling magnetic embolic material more smoothly towards an inner wall ofan aneurysm) such a transverse gradient has been found to beadvantageous.

[0179] According to this aspect of the invention, the magneticnavigation is supplemented by the application of the magnetic gradient.In some instances the application of the magnetic gradient assists innavigation, in other instances, the gradient is not applied to assistnavigation, but to otherwise exert a pulling force on the magneticmedical device.

[0180] There are many instances where it would be desirable to exert apulling force after a magnetic medical device has been navigated to aparticular position in the body. For example, in the case of treatinganeurysms, a magnetic pulling force could be applied after navigation ofa magnet tip to a given location, for pulling magnetic embolic materialsinto an aneurysm. (The magnetic medical device may or may not be removedfrom the area before applying the pulling force). Either a transverse orlongitudinal gradient may be used. If no subsequent navigation orsignificant turning of the orientation of the magnetic medical device isrequired, the computer processor 22 which controlled the initialnavigation will have information not only about the orientation of themagnet tip 46, but about the orientation of the source magnetic fieldand gradient. That is, the processor will have information whether, atthe operating point 42, the gradient is transverse or longitudinal.According to this aspect of this invention, the physician will, at thestart of the procedure, input the desired method of using the gradient,and therefore at the completion of navigation (and after removal of themagnet tip, if necessary) the source magnet 38 will be oriented so thatthe gradient is in the desired direction.

[0181] At this point, a gradient must be established in the desireddirection of pulling (e.g., the back wall of an aneurysm in anembolization procedure, or the wall of a heart chamber in an EP(electrophysiology) procedure). The processor 22 will have informationabout the current state of the magnetic field and gradient. Given thedesired state of the relative directions of magnetic field and gradient,the processor can determine and direct a movement of the source magnetfor the purpose of changing the direction of the gradient relative tothe direction of the field, or vice versa. This relative movementbetween gradient direction and field direction is called a “gradientturn”.

[0182]FIG. 15A shows a cross section of an aneurysm with a magneticfield B represented by field lines pointing away from the back wall ofthe aneurysm, and a magnetic gradient represented by a double arrow,pointing toward the back wall of the aneurysm. In certain embolizationprocedures, it is desirable that the applied magnetic field be parallelto the neck of the aneurysm and perpendicular to a magnetic gradientthat is oriented toward the back wall of the aneurysm. This builds alayered embolism in the aneurysm. As shown in FIG. 15B, after a gradientturn the magnetic field B represented by field lines pointing parallelto the neck of the aneurysm, is now perpendicular to magnetic gradient,represented by the double arrow, pointing toward the back wall of theaneurysm. While it is apparent from FIG. 14, and equation (21) what thegradient direction will be at these starting and ending locations, it isnot apparent how the field and gradient directions relate at theintervening locations, nor how to use equation (21) to determine thegradient changes during that transition. The execution of a “gradientturn” above, will require a knowledge of the projection of B on m.

[0183] The requirement, then, is for the processor 22 to determine themovements of the source magnet 38 necessary to perform the gradient turnin the coordinate system of the patient. FIG. 14 shows a gradual changein the spacing of lines moving from a longitudinal gradient at point Ato a transverse gradient at point B. That is, there can be a gradualchange in the gradient of the scalar product m. B since m is fixed inmagnitude and the line spacing is proportional to the magnitude of B. Asdiscussed above, the navigation program implemented by the processorcontains either an equation or a lookup table for the source magneticfield B of the magnet in the source magnet coordinate system. Thelocation of the magnet tip 46 in the patient coordinate system istransformed into the source magnet coordinate system as described inearlier, so that B is known at the operating point 42 in the patientcoordinate system from a further inverse transformation. The force Ffrom equation (1) is determined from this information, knowing m, forthe current source magnet position and orientation, and for a series oftrial rotations and translations. The only additional requirement isknowledge of, or an assumption of, the direction of m during thegradient turn. From these trial calculations, the choice of a gradientturn of the source magnet is made in the same manner as was describedfor a safe navigation turn above. If, due to limitations in accuracy,there is significant error in assumed change in the direction of m, itmay or may not be necessary for a locator or imaging system to measurethe change in direction and update the processor.

[0184] In all but unusual conditions, the procedure described above isconceptually simple, since m. B varies as mB cos θ, where θ is the anglebetween m and B. The direction and magnitude of m in the patientcoordinate system will not change significantly in the types ofnavigation likely to be used. However, due to the transformationsbetween coordinate systems the quantity cos θ will change from 1 to 0 asthe source magnet is moved (in the example illustrated in FIGS. 15A and15B) so that the transformed operating point 42 moves from a point onthe axis of the source magnet axis to a point on its equatorial plane inthe source magnet coordinates, that is θ goes from 0 degrees to 90degrees. In the process, the quantity B will change in the patient,since the side field of the source magnet is less than the axial fieldof the source magnet, at a given distance. This may be not important,since the field strength for pulling a magnetic material into ananeurysm will be separately input by special requirements. To fulfillthe needed change in the strength of B, the source magnet 38 will betranslated closer to or further from the operating point 42 in thepatient.

[0185] In another embodiment, such as the orienting and pulling of amagnet-tipped electrode against an interior heart chamber wall, it maybe necessary to retain an orienting magnetic field in a directionapproximately parallel to the wall, while exerting a pulling gradientapproximately towards the wall. This may occur in a manner in which themagnet tip or tip ensemble on the electrode have in their design thecapability of responding directly to a transverse gradient, and notresponding in that manner to a longitudinal gradient. Special tipdesigns are needed, such as described in U.S. patent application Ser.No. 09/311,686, filed May 13, 1999, for Magnetic Medical Device andMethod of Navigating Magnetic Medical Devices with Magnetic Fields andGradients, incorporated herein by reference. In such a case, informationspecific to the design of the particular magnetic tip 46 will have beenentered in the processor 22 at the start of the procedure. The magnetictip 46 will be navigated to the procedure location, such as a chamber ofthe heart, in a manner similar to that of a simple magnet tip. When thetip has been navigated to the desired point, the source magnet can beturned so as to progressively move the gradient from longitudinal totransverse, while holding the tip against the wall, as described above.While changing the gradient direction, the magnet tip 46 is held towardsthe wall by applying a torque with the magnetic field direction. Themagnet tip 46 is held against the wall in this manner while the gradientis being applied to pull the magnet tip toward the wall. In essence,there is a continuous transition from a guidance-dominant situation to apull-dominant situation.

[0186] One embodiment of system for carrying out navigations inaccordance with the methods of this invention is indicated generally as200 in FIGS. 7A and 7B. The system 200 comprises a patient bed 202 forsupporting the patient, an imaging system 204 for providing images ofthe operating region within a patient on the patient bed 202, and amagnet system 206 for projecting magnetic fields and gradients into theoperating region in a patient on the patient bed 202.

[0187] The imaging system 204 comprises a C-arm apparatus 208, mountingtwo pairs of imaging beam source 210 and imaging plates 212, which arepreferably mutually perpendicular. The C-arm apparatus includes agenerally L-shaped support 214 that is mounted on base 216 for pivotingabout a generally vertical axis, an intermediate support 218 that ismounted on L-shaped support for rotation about a generally horizontalaxis; and a C-shaped bracket 220 that is mounted on the intermediatesupport for rotation about the central axis of the C-shaped bracket.

[0188] The magnet system 206 comprises a source magnet 222 and anarticulation device 224 for translating and rotating the source magnet222. The source magnet is preferably a superconducting electromagnet,with associated cryocooler 226. The housing conventionally used isomitted to show the configuration of the magnet. The articulation device224 provides movement of the magnet 222 with three degrees of freedom(two rotations and one translations). The articulation device 224comprises a base 228 that is mounted on tracks 230 for translationtoward and away from the patient bed, thereby allowing translation ofthe magnet 222 toward and away from the operating region within apatient on the patient bed 202 (i.e. along the z axis as describedabove). The articulation device 224 includes a C-shaped arm 232, that ismounted on the base 228 for rotation about a first generally horizontalaxis, which allows a first rotation of the magnet 222. The magnet 222 isalso mounted to the C-shaped arm 232 for rotation about a second axisgenerally perpendicular to the first generally horizontal axis, whichallows a second rotation of the magnet.

[0189] The movement of the base 228 on the tracks 230, rotation of theC-shaped arm 232 relative to the base, and the rotation of the magnet222 relative to the C-shaped arm provides magnet motion with threedegrees of freedom, and each of these movements can be controlled by amicroprocessor as described herein, to project a desired magnetic fieldand or gradient into an operating region within a patient on the patientsupport.

[0190]FIG. 7B shows the system 200 with a surface 234 of constant fieldstrength projected around the magnet 222. In navigations using thisconstant field strength, it is apparent there is at least onesignificant exclusion zone surrounding the location where the cryocooler226 projects through the surface 234. Rotations and translations thatwould attempt to bring this exclusion zone to the operating regionwithin the patient must be prohibited, because the cryocooler wouldstrike the patients. Other rotations and translations that would bringthis exclusion zone into contact with other structures in the operatingroom, for example with the imaging system 204 or the articulation device224, or interfere with the imaging beams from the imaging system 204,must also be prohibited as described below.

[0191] Another embodiment of system for carrying out navigations inaccordance with the methods of this invention is indicated generally as300 in FIGS. 7C through 71. The system 300 comprises a patient bed 302for supporting the patient, an imaging system 304 for providing imagesof the operating region within a patient on the patient bed 302 patient,and a magnet system 306 for projecting magnetic fields and gradientsinto the operating region in a patient on the patient bed 302.

[0192] The imaging system 304 comprises a C-arm apparatus 308, mountingtwo pairs of imaging beam source 310 and imaging plates 312, which arepreferably mutually perpendicular. The C-arm apparatus includes agenerally L-shaped support 314 that is mounted on base 316 for pivotingabout a generally vertical axis, an intermediate support 318 that ismounted on L-shaped support for rotation about a generally horizontalaxis; and a C-shaped bracket 320 that is mounted on the intermediatesupport for rotation about the central axis of the C-shaped bracket.

[0193] The magnet system 306 comprises a source magnet 322 and anarticulation device 324 for translating and rotating the source magnet322. The source magnet 322 is preferably a superconductingelectromagnet, with associated cryocooler 326, the magnet is surroundedby a housing 328. The articulation device 324 provides movement of themagnet 322 with five degrees of freedom (three rotations and twotranslations). The articulation device 324 comprises a base 330 that ismounted on tracks 332 for translation toward and away from the patientbed 302, thereby allowing translation of the magnet 322 toward and awayfrom the operating region within a patient on the patient bed 302 (i.e.,along the z axis as described above). A turntable 334 is mounted on thebase 330 for rotation about a generally horizontal axis. The turntable334 has a track 336 extending diametrically across it for slidablymounting a support arm 338, so that the support arm can translate withinthe track. The magnet is mounted on the end of the support arm. Morespecifically a C-shaped arm 340 is mounted on the end of the support arm338, for rotation about a first axis. The magnet 322 is mounted to theC-shaped arm 340 for rotation about a second axis generallyperpendicular to the first axis.

[0194] The movement of the base 330 on the tracks 332, rotation of theturntable 334 relative to the base, the translation of the support arm338 relative to the turntable 334, the rotation of the C-shaped arm 340relative to the support arm, and the rotation of the magnet relative tothe C-shaped arm provides magnet motion with five degrees of freedom,and each of these movements can be controlled by a microprocessor asdescribed herein, to project a desired magnetic field and or gradientinto an operating region within a patient on the patient support.

[0195]FIG. 7E shows the system 300 with a work envelope 350 surroundingthe patient, defining the volume in which the articulation device 324can translate the magnet 322. FIG. 7F shows the system 300 illustratingthe range of motion of magnet, illustrating a maximum 360 degreerotation of the magnet 322 about the C-shaped 340 (not shown in FIG.7F), and a maximum 180 degree rotation of the C-shaped arm 340, relativeto the support arm 338.

[0196]FIG. 7G shows the system 300 illustrating a magnet work envelope352 within which the magnet 322 can be translated and the sweep volume354 that must be clear to accommodate the cryocooler 324 as the C-shapedsupport arm 340 and the magnet 322 rotate for a given translationalposition of the magnet in the work envelope 352. FIG. 7H shows thesystem 300 illustrating a rotation of the magnet 322 to provide accessfor the magnet to project the desired magnet field and/or gradient inthe operating region in a patient on the patient bed 302. FIG. 71 showsthe system 300 and illustrates the clearance between the work envelopearound in the patient in which the magnet 322 moves, and the support forthe imaging system.

[0197] In navigations using the system 300, it is apparent there aresignificant limitations on the positions and orientations of the magnetto avoid contact with the patient, other equipment in the operatingroom, and imaging beams from the imaging apparatus. These limitationscan be addressed using exclusion zones, as described in more detailbelow.

[0198] Use of Exclusion Zones

[0199] For some of the procedures for which the magnetic navigationmethod of the present invention may be employed, there will becongestion in the region surrounding the patient, making it difficult toarticulate a source magnet in ways desired to provide guiding fields inall needed directions and at required magnitudes. Primarily, the magnetand its accoutrements cannot be translated or rotated in such a way thatthey impinge upon the patient or any of surrounding medical equipment,including for example the patient bed and the imaging equipment, orinterfere with the imaging beams. The processor 22 can control themovement of the source magnet 38 so that the interference does notoccur, and can even anticipate interferences for a planned path of anumber of turns for the navigated object.

[0200] The processor 22 can determine the necessary safe and efficientsteps, or component parts of a step, in a path of navigation. Each suchstep requires rotation and/or translation of the source magnet, and theprocessor calculates these by transforming the desired step, in thepatient reference frame, to its geometrical counterpart in the sourcemagnet reference frame, and calculates efficient and safe source magnetmotions to accomplish the field changes in the patient reference frame,as described herein. The following steps can be implemented to avoidthese interferences:

[0201] The geometric “edge” of the patient, imaging equipment, etc. onthe side facing the source magnet 38, can be thought of as a somewhatcomplex “sheet”. This sheet can be defined in the coordinates of thepatient reference frame by a set of vectors from the origin of thatframe to appropriate points on the “patient sheet”. The number anddistribution of these vectors can vary, depending on the complexity ofthe sheet and the desired geometrical resolution in its description.Nevertheless, they can be stored in the processor memory, for example asa look-up table, or instead as a set of equations for geometricalobjects.

[0202] Similarly, a “source magnet sheet” can be described in thearticulatable (moveable) magnet reference frame as a set of vectors inthose coordinates. On any anticipated move of the source magnet 38, theprocessor 22 can test for overlap or touching of the two sheets bytransforming either one to the reference frame of the other. Moreover,the processor can determine (and present on a display if desired) theclosest distances if there is not yet an interference.

[0203] When these “tests” are applied to an articulation which is usedto place a vector magnetic field in the patient, there are a number ofways of accomplishing the desired directional change of the magneticfield, some more geometrically efficient than others. The injection ofinterference avoidance as a constraint on possible articulations mustthen be combined with the vector field properties of the magnet intesting for alternate articulation in any given desired move.

[0204] The specific steps involved in this combination will depend onthe number and types of degrees of freedom of the articulation mechanism36. Specifically: (A) A 3-degree of freedom system will have noavailable redundancy for a single move. In such cases multiple movesmust be planned ahead for interferences, if necessary using tolerancesin the provided field direction. (B) Systems with 4 or more degrees offreedom can have remaining choice(s) for each specific move. Among otherthings, these choices offer different angles for the “magnet sheet” toapproach the “patient sheet”. They can offer alternate articulations fora given planned path without using field direction tolerance.

[0205] The way this can be put into the navigation trial solutions isshown in FIG. 10, in which “trial” moves shown as P_(i), and P_(n), etc.are rotations and/or translations of the source magnet 38 which will beable to make a given direction change of the field B in the patient(given sufficient number of degrees of freedom) at the point operatingpoint 42 where the magnet tip 46 is to be navigated, while maintaining aconstant field magnitude B.

[0206] Given the patient and source magnet sheets as previouslydescribed, the processor 22 will be able to determine regions of theseP_(i) directions which are not permissible for a proposed turn, andthereby restrict the solution set. It is to be understood that each ofthese vectors P_(i) corresponds to the same or nearly the same turn of Bin the patient, and they differ only in the way they use the excessdegrees of freedom of the articulation mechanism 36. (A result of thiswill be a change in the “efficiency” of the turn which can be defined asthe amount of turning and translating of the source magnet to providesuch a safe and correct (planar) turn of the vector B in the patient.)

What is claimed is:
 1. A method of turning a medical device, having amagnetically responsive element associated with its distal end, at anoperating point within an operating region inside a patient's body froman initial direction to a desired final direction, through the movementof at least one external source magnet, the method comprising: movingthe at least one external source magnet in such a way as to change thedirection of the distal end of the magnetic medical device from theinitial direction to the desired final direction without substantialdeviation from the plane containing the initial direction and thedesired final direction.
 2. The method according to claim 1 wherein themovement of the at least one source magnet comprises translations androtations.
 3. The method according to claim 2 wherein the movement ofthe at least one source magnet includes translation in one direction androtations in two directions.
 4. The method according to claim 1 whereinthe at least one source magnet is moved in such a way as to maintain asubstantially constant magnetic field strength at the operating point.5. The method according to claim 1 wherein the step of moving the atleast one external source magnet includes moving the at least oneexternal source magnet to cause the distal end of the magnetic medicaldevice to successively align with a plurality of intermediate directionsin a plane containing the initial direction and the desired finaldirection.
 6. The method according to claim 5 wherein the movement ofthe at least one source magnet comprises translations and rotations. 7.The method according to claim 5 wherein the at least one source magnetis moved in such a way as to maintain a substantially constant magneticfield strength at the operating point.
 8. A method of turning a medicaldevice, having a magnetically responsive element associated with itsdistal end, at an operating point within an operating region inside apatient's body, from an initial direction to a desired final direction,through the movement of at least one external source magnet, the methodcomprising: moving the external source magnet to cause the distal end ofthe magnetic medical device to successively align with each of aplurality of intermediate directions and the desired final direction,while maintaining a substantially constant magnetic field strength.
 9. Amethod of turning a medical device, having a magnetically responsiveelement associated with its distal end, at an operating point within anoperating region inside a patient's body from an initial direction to adesired final direction, through the movement of at least one externalsource magnet, the method comprising: identifying a series ofintermediate directions between the initial direction and the desiredfinal direction, each intermediate direction being substantially in theplane containing the initial direction and the desired final direction;determining the magnetic field direction at the operating point thatwill cause the magnetically responsive element to align with each ofseries of intermediate directions and the desired final direction;successively moving the at least one source magnet to apply thedetermined magnetic field directions to align the magnetic medicaldevice with each of the series of intermediate directions and thedesired final directions.
 10. The method according to claim 9 whereinthe step of successively moving the at least one source magnet to applythe determined magnetic field directions to align the magnetic medicaldevice with each of the series of intermediate directions and thedesired final directions is done to so that the magnetic field strengthat the operating point remains substantially constant.
 11. The methodaccording to claim 9 further comprising the step of determining therequired movements of the at least one source magnet before moving theat least one source magnetic, and testing the required movements bycalculating the amount by which the direction of the magnet medicaldevice would from the plane of the initial direction during thedetermined required movements, and identifying a different series ofintermediate directions if the variation exceeds a predeterminedthreshold.
 12. The method according to claim 9 wherein the step ofmoving the at least one source magnet comprises determining anorientation of the at least one source magnet to apply the determinedfield direction.
 13. The method according to claim 12 wherein the stepof determining the orientation of the at least one source magnet toapply the determined field direction employs a look-up table.
 14. Themethod according to claim 12 wherein the step of determining theorientation of the at least one source magnet to apply the determinedfield direction employs an equation characterizing the magnetic field ofthe source magnet.
 15. The method according to claim 9 wherein themovement of the magnet from one position to another position is made bytaking a number of trial movements in a plurality of differentdirections and testing the movement.
 16. The method according to claim 9wherein the step of identifying the magnetic field direction that willcause the magnetic medical device to align with each of the intermediatedirections and the desired final direction, takes into account the lagbetween the applied magnetic field and the actual orientation ofmagnetic medical device.
 17. The method according to claim 16 whereinthe step of identifying the magnetic field direction that will cause themagnetic medical device to align with each of the intermediatedirections and the desired final direction employs an equation todetermine the lag between the applied magnetic field and the actualorientation of magnetic medical device.
 18. The method according toclaim 16 wherein the step of identifying the magnetic field directionthat will cause the magnetic medical device to align with each of theintermediate directions and the desired final direction employs alook-up table to determine the lag between the applied magnetic fieldand the actual orientation of magnetic medical device.
 19. The methodaccording to claim 9 wherein identifying the magnetic field directionthat will orient the magnetic element to align with each of theintermediate directions and the desired final direction is determinedwith an appropriate over-torque.
 20. The method according to claim 9further comprising computing the amount by which the magnetic medicaldevice deviates from the plane containing the initial direction andfinal direction, and identifying a new series of intermediate directionsif the deviation exceeds a predetermined threshold.
 21. The methodaccording to claim 20 wherein the step of identifying a new series ofintermediate directions comprises identifying intermediate directionsbased upon the direction in which the deviation of the magnetic medicaldevice from the plane of the initial direction and the desired finaldirection exceeds a predetermined amount.
 22. The method according toclaim 9 wherein the desired final direction and the series ofintermediate directions are identified in the patient frame ofreference, and translated to the frame of reference of the at least onesource magnet.
 23. The method according to claim 9 wherein there is alook-up table of prohibited movements of the at least one source magnet,and the look-up table is referenced before moving the source magnets.24. The method according to claim 9 wherein several possible movementsof the at least one source magnet are determined, and the actualmovement selected is selected based upon minimizing the cost functionfor the movement of the at least one source magnet.
 25. A method ofturning a magnet element at an operating point inside the body from aninitial direction to a desired final direction by moving a source magnetoutside the body, the method comprising the steps of: determining aseries of movements of the source magnet to turn the magnetic element tosuccessively align with a series of target directions including at leastone intermediate direction between the initial direction and the desiredfinal direction, and the desired final direction, such that thedirection of the magnetic element during each movement of the sourcemagnet in the series does not deviate from the plane of the initialdirection and the desired final direction by more than a predeterminedamount; and implementing the determined movements of the source magnetin series to turn the magnetic element from the initial direction to thefinal direction through the at least one intermediate direction.
 26. Themethod according to claim 25 where the step of determining the series ofmovements comprises: (a) selecting an initial series of targetdirections; (b) determining the magnet movements needed to apply amagnetic field to turn the magnetic element to the target directionsfrom their respective prior directions, and testing whether suchmovement causes the direction of the magnetic element to deviate fromthe plane of the initial direction and the final desired direction bymore than a predetermined amount, and if so, selecting new and/oradditional intermediate directions for the series of target directions;(c) repeating step (b) until series of target directions andcorresponding magnet movements have been determined that do not causethe direction of the magnetic element to deviate from the plane of theinitial target direction by more than a predetermined amount.
 27. Amethod of turning a magnet element at an operating point inside apatient's body from an initial direction to a desired final direction bymoving a source magnet outside the body, the method comprising the stepsof: (a) providing means for determining and maintaining during aprocedure the location and orientation of the magnet element relative tothe location and orientation of the external source magnet; (b) choosingdesired field vectors in the patient frame as a series of angularlyspaced vectors which lie in the plane of the initial and final vectorsand entering them in a processor; (c) entering the position anddirection of the vectors into a processor by a means of specifying anddisplaying the field and communicating with the processor; (d)calculating field directions at the operating point in the referenceframe of the patient by translating the desired vectors into thereference frame of the magnet; (e) transforming each one of the sequenceof vectors into the reference frame of the source magnet; (f)calculating a surface of constant field strength of desired value in themagnet frame; (g) locating each of the field vectors on the appropriatelatitude of the surface of constant field strength corresponding to thecorrect transformed direction of the field vector; (h) for each pair ofsequential vectors of the total set, calculating the minimum motion ofthe source magnet required to change the field direction, takingadvantage of the azimuthal symmetry of the magnet field; and (i)executing the desired step turns by articulating the source magnet. 28.The method of claim 27 in which the articulation of the source magnetuses coordinated translations and rotations to maintain a turn nearly ina plane.
 29. The method of claim 27 in which the magnet element isattached to a medical device.
 30. The method of claim 29 in which themagnet element is attached to a catheter.
 31. The method of claim 29 inwhich the magnet element is attached to an endoscope.
 32. The method ofclaim 29 in which the magnet element is attached to an electrode. 33.The method of claim 27 in which the magnet element is attached to aguide wire.
 34. The method of claim 27 in which the desired turn of themagnet is in a body lumen in a patient.
 35. The method of claim 27 inwhich the desired turn of the magnet is in body tissue in a patient. 36.The method of claim 27 in which exclusion zones are entered into, andremain in the processor as vectors in the patient reference frame andtransformed into the magnet frame so the processor can use them inproviding the proper requested turns while avoiding interferences. 37.The method of claim 27 in which calculations of possible vectors with agiven angular resolution are made in advance and entered into lookuptables.
 38. The method of claim 27 in which the execution of the stepturns is the articulation of a single magnet.
 39. The method of claim 27in which the spacing of the desired intermediate vectors of a turn ischecked in the processor for departure of motion from a plane in thepatient frame.
 40. The method of claim 27 in which the calculation andexecution of the step turns is the articulation of at least two magnets.41. The method of claim 36 in which the exclusion zone includes both theinterfering objects or beams in the patient frame and those on thearticulated magnet.
 42. The method of claim 27 in which turn limitationsof the source magnet, such as those from leads, are included in the turncalculations of the processor.
 43. The method of claim 29 in which thevectors calculated for turns take into account the departure of themagnet element in the patient from a field line which is caused bystiffness of the attached medical device to the magnet element.
 44. Themethod of claim 27 in which the friction of a medium in which the turnoccurs is taken into account.
 45. The method of claim 29 in which alocating system provides information about the location, orientation,and twist of the medical device to which the magnet tip is attached. 46.The method of claim 45 in which the measured twist of the lumen tip isused to provide a display of the internal view from the medical devicelumen, corrected for that twist, to the physician.
 47. The method ofclaim 29 further comprising imaging through the medical device, andproviding an intuitive interface so internal viewing through the medicaldevice can be used to navigate the magnet element.
 48. The method ofclaim 47 in which the navigation interface includes the ability torotate about the axis of the lumen for complete inspection of the lumen.49. The method of claim 47 in which the navigation includes the abilityto rotate about the axis of the lumen to provide treatment at a desiredpoint on the wall of the lumen.
 50. The method of claim 27 in which thelocating and orienting means is magnetic.
 51. The method of claim 52 inwhich during articulation of a source magnet the processor usesinformation on the magnet element from imaging or a locator to correctfor departure of the observed motion from that requested.
 52. A methodof navigating a small magnet in a patient using articulation of anexternal magnet source field, in which the navigation algorithmmaintains the field magnitude substantially constant at the position ofthe small magnet during the navigation.
 53. A method of navigating asmall magnet in a patient using articulation of an external magnetsource field, in which the navigation algorithm uses the symmetry of thesource magnet to achieve solutions which will minimize computer memoryand time.
 54. A method of navigating a small magnet in a patient usingarticulation of an external magnet source field, in which the navigationalgorithm uses the symmetry of the source magnet to achieve solutionswhich will minimize source field magnet articulation time.
 55. A methodof navigating a small magnet in a patient using articulation of anexternal magnet source field, in which the navigation algorithm usescorrective feedback to reduce the need for precise characterization ofdistances and physical parameters while maintaining safe, efficientnavigation.
 56. A method of navigating a small magnet in a patient usingarticulation of an external magnet source field with one translationaxis and two rotation axes of the articulator.
 57. An articulationalgorithm for providing a magnetic field in any direction at anylocation in a patient operating region by translating a magnet along apatient body axis, and rotating the magnet.
 58. A method of turning amedical device having a magnetically responsive element associated withits distal end, at an operating point within an operating region insidea patient's body from an arbitrary first orientation to an arbitrarysecond orientation, the method comprising moving at least one sourcemagnet in one direction of translation and two directions of rotation.